1 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.01 Experiment 03: Work and Energy Purpose of the Experiment: In this experiment you allow a cart to roll down an inclined ramp and run into a spring that is attached to a force sensor. You will measure the position of the cart and the force exerted on it by the spring while they are in contact. It is a “real world” experiment, which means that there are non-conservative forces: friction as the cart rolls up and down the track, and dissipation (internal friction?) in the spring. The goals of the experiment are: • To investigate experimentally the work–kinetic energy theorem, how potential energy in a gravity field converts to kinetic energy which is then converted into the potential energy of a compressed spring. • To observe and quantify the effect of non-conservative forces and estimate the work done by these forces at various stages of the cart’s motion up and down the ramp. Setting Up the Experiment: Refer to the photo to the right and the figure at the top of the next page. A force sensor should be mounted at the end of the track that has an adjustable support screw—which should be screwed in enough that the end of the track can lie flat on the table. Clip the motion sensor to the other end of the track and raise it by placing a short piece of 2×4 under the motion sensor where it clips onto the track, as you can see in the photo to the right. This should raise the end of the track about 4.2 cm above the table; as the track is 122 cm long, you can calculate the slope 1.97θ=D and sin 0.0344θ= . The motion sensor works best if it is aimed slightly above the center of the cart rather than pointing directly at it. (That reduces the effect of sound waves that bounce off the2 track before hitting the cart.) The slide switch on top of the motion sensor should be set to the narrow beam position. Usually two springs are available to screw into the force sensor; if so, use the one that is wound from thinner wire. Place a cart on the track with the end having the VelcroTM patches facing the motion sensor. Put two 250 gm weights in the cart, which will bring its total mass to 750 gm. (The extra mass reduces vibrations and gives less noisy measurements.) Place the cart about 30 cm up the track from the force sensor and release it. It will roll down the track, bounce most of the way back up, and repeat that several times. You will notice the track slides when the cart runs into the spring; this is an example of conservation of momentum. To prevent the track from sliding, place your thumb on the end of the track resting on the table and press it firmly against the table. If you don’t do this, when the cart runs into the spring some of its kinetic energy will be dissipated by friction of the track on the table—which will introduce an unknown error in your analysis. Connect the motion sensor (yellow plug into jack 1, black plug into jack 2) and the force sensor to the SW750 interface. The force sensor should be plugged into channel A of the SW750. Be sure to tare the force sensor before each measurement. The LabVIEW Program WorkEnergy: The LabVIEW program you will use in this experiment is called WorkEnergy. Like our other LabVIEW programs, it is controlled by a pull-down menu above the left side of the graph. There is also a pull-down menu to control plotting of data. The program has two tabs. The Table&Fits tab displays a table of the data plotted on the graph and allows you to control the fits the program can do. It also displays the numerical results of the fits.3 The Sample Rate should be set to 100 Hz (this is the rate the position of the cart is measured at; the force will be measured 10 times more often). Set the Run Time to 12 s. In the experiment you will let the cart roll into the spring starting from rest about 30 cm up the track from the point where it first touches the spring. Try this to see how things behave. When you are ready to measure, hold the cart in position, and choose Measure from the pull-down menu. The RUN button will change to bright green. Be sure to hold the track so it will not slide and click the RUN button (or type the Esc key) and release the cart at about the same time. After the 12 s have elapsed, you should see a graph of raw data something like this one. The top curve is the echo delay of the ultrasonic pulse from the cart to the motion sensor and the bottom curve is the voltage output of the force sensor. These are the raw data, and you may save them to a file in the 8.01 course locker for later analysis. You can see from the peaks in the lower curve the times when the cart bounces off the spring and you can see from the upper curve that the cart bounces back up to a lower height each time. You should analyze these raw data in several different ways. The program computes the position, velocity, and acceleration of the cart using the Savitzky-Golay method discussed in the notes for Experiment 1. You may plot any of these three quantities as a function of time by choosing what you want from the Plot Control pull-down menu and then clicking the Replot button; you may also plot the force alone as a function of time.4 You will need to use the cursors and frequently expand the X (time) scale on the graph to carry out the analysis of your results. If you need a reminder of how to do this, the LabView graph controls are discussed in an appendix. Each graph has two cursors, which you will use to select which data points will be fit by the functions that are available and also to determine the numerical x and y positions of points on the graph. Position the cursors by dragging them when the cursor (left) button is selected on the graph control palette. Part One: Analyzing Your Measurement: First, make a plot of position vs. time; it should look something like the one below. Carry out your analysis around the second bounce of the cart off the spring. The cart started a height 1h above the spring and then bounced back up to a lower height 2h . Obviously some energy was lost. Use the cursors and the cursor position readouts5 above the graph to find 1h and 2h ; first measure the positions of the cart when it is closest to the motion sensor at the turning points on either side of the second bounce. You may be tempted to determine 1h and 2h from the lowest point of the cart during the bounce. However, that will introduce a significant
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